Un-knots

I’ve been making some diagrams, diagram-drawings. I realised whilst making these that they are all un-knots – so long as I carried on drawing my new line crossing beneath everything that was already there, i.e. being the broken line, they always would represent un-knots – disentangle completely to leave nothing but a loop. To make a knot that does anything more interesting, then, the drawer must at some point place their line over an earlier piece of line, which is what requires the odd process of either earlier on leaving a gap for a line to then cross over (often imperfectly), or erasing the line that’s already there. That requires a temporal disruption, a glitch in the sequence of the drawing, and neither of those gap-leaving devices works particularly comfortably.

The thing I’m abandoning here is the requirement for economy in a useful knot diagram. Relevance Theory – these include a lot of detail and swoops and crossings that really aren’t relevant, that provide all sorts of useless extra information that needs processing but offers a whole lot of no benefit. One of them I’ve even abandoned the smooth lines. Ouch.

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One thought on “Un-knots

  1. Unknots – as they are they give the impression (to me without my glasses) of being knotted as I can’t easily see the erased (or not drawn) sections. With my glasses and avoiding the illusion that they are knotted, then they are actually a collection of lines or strings of various lengths. I wonder, if the lines were hard so their length and bends were fixed, they could be rearranged into any more convincing impressions of knotted things – other than just mirroring them… Sent from my BlackBerry 10 smartphone. From: An Artist Explorer in MathematicsSent: Thursday, 14 April 2016 15:55To: poolphilip@yahoo.co.ukReply To: An Artist Explorer in MathematicsSubject: [New post] Un-knots

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    katiemccallum posted: ”

    I’ve been making some diagrams, diagram-drawings. I realised whilst making these that they are all un-knots – so long as I carried on drawing my new line crossing beneath everything that was already there, i.e. being the broken line, they always would r”

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